Rigorous solutions of wave equation are highly accurate in simulating wave propagation through complex subsurface regions. Downward continuation methods based on the one-way wave equation are well known for their computational efficiency and accuracy in handling multi-path events. Reverse-time migration (RTM) offers additional advantages over one-way imaging by removing the dip limitation and therefore is capable of handling wave propagation in any direction. Consequently a more complete set of waves (for example, prismatic waves, overturning waves and potentially multiples) can be used constructively for imaging challenging subsurface structures, such as steeply dipping or overhanging salt flanks. Although becoming increasingly affordable, RTM is generally considered more computationally intensive than one-way downward continuation methods.
The high computational cost of RTM arises from solving the two-way wavefield propagation. For example, the source wavefield is propagated over time and saved to an electronic storage medium. As a result, RTM requires a significant storage space for reverse-time access of 3D source wavefields unless wavefield storage is traded with increased computation time. In RTM, in addition to the forward wavefield propagation, the seismic data are back extrapolated and correlated with the source wavefield. The runtime cost of RTM is thus approximately twice that of forward full-wavefield modeling.
Several prior art methods have been proposed to make RTM more efficient for practical applications in recent years. One prior art method shows that RTM is equivalent to Generalized Diffraction Stack Migration (GDM). A reduced version of GDM, called wavefront wave-equation migration, uses only first-arrival information to back-propagate arrivals. By introducing a square-root operator, another prior art method shows that the two-way wave equation can be formulated as a first-order partial differential equation (PDE) for cost-effective implementation. Yet another prior art method suggests target-oriented reverse time datuming (RTD) by extrapolating wavefields to a subsalt artificial datum using a finite-difference solver. Below the datum, a less intensive imaging method such as Kirchhoff migration can be used. Most recently, another prior art method showed test examples of target-oriented RTD. There, however, still exists a need for methods which perform RTM in less-costly computational ways.